In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is −∆pu = β|∇u|q + c|u|p−2u + f in Ω, u = 0 on ∂Ω, where Ω is an open bounded subset of RN, N ≥ 2, 1 < p < N, ∆pu is the so-called p-Laplace operator, and p − 1 < q < p. We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem.
On a Class of Nonlinear Elliptic Equations with General Growth in the Gradient
Maria Francesca Betta;
2024-01-01
Abstract
In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is −∆pu = β|∇u|q + c|u|p−2u + f in Ω, u = 0 on ∂Ω, where Ω is an open bounded subset of RN, N ≥ 2, 1 < p < N, ∆pu is the so-called p-Laplace operator, and p − 1 < q < p. We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem.File in questo prodotto:
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